9) The following results are from a regression where the dependent variable is GRADUATION RATE and the independent variables are % OF CLASSES UNDER 20, % OF CLASSES OF 50 OR MORE, STUDENT/FACULTY RATIO, ACCEPTANCE RATE, 1ST YEAR STUDENTS IN TOP 10% OF HS CLASS. The data were split into 2 samples and the following regression results were obtained from the split data. a) What is heteroscedasticity? (b) Why is heteroscedasticity a problem? c) Based on a comparison of the two sets of output, does it appear that there is heteroscedasticity in the data set? Explain. Be sure to write down your null and alternative hypothesis, calculate the test statistic, and find your critical value (test at the 5% level of significance).
9) The following results are from a regression where the dependent variable is GRADUATION RATE and the independent variables are % OF CLASSES UNDER 20, % OF CLASSES OF 50 OR MORE, STUDENT/FACULTY RATIO, ACCEPTANCE RATE, 1ST YEAR STUDENTS IN TOP 10% OF HS CLASS. The data were split into 2 samples and the following regression results were obtained from the split data. a) What is heteroscedasticity? (b) Why is heteroscedasticity a problem? c) Based on a comparison of the two sets of output, does it appear that there is heteroscedasticity in the data set? Explain. Be sure to write down your null and alternative hypothesis, calculate the test statistic, and find your critical value (test at the 5% level of significance).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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9) The following results are from a regression where the dependent variable is GRADUATION RATE and the independent variables are % OF CLASSES UNDER 20, % OF CLASSES OF 50 OR MORE, STUDENT/FACULTY RATIO, ACCEPTANCE RATE, 1ST YEAR STUDENTS IN TOP 10% OF HS CLASS. The data were split into 2 samples and the following regression results were obtained from the split data.
a) What is heteroscedasticity?
(b) Why is heteroscedasticity a problem?
c) Based on a comparison of the two sets of output, does it appear that there is heteroscedasticity in the data set? Explain. Be sure to write down your null and alternative hypothesis, calculate the test statistic, and find your critical value (test at the 5% level of significance).
Transcribed Image Text:9) The following results are from a regression where the dependent variable is GRADUATION RATE
and the independent variables are % OF CLASSES UNDER 20, % OF CLASSES OF 50 OR MORE,
STUDENT/FACULTY RATIO, ACCEPTANCE RATE, 1ST YEAR STUDENTS IN TOP 10% OF HS
CLASS. The data were split into 2 samples and the following regression results were obtained from
the split data.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.588
R Square
0.346
Adjusted R Square
0.044
Standard Error
4.55
Observations
20
ANOVA
df
SS
MS
Significance F
Regression
142.0
23.7
1.15
0.391
Residual
13
268.8
20.7
Total
19
410.8
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
86.8
25.9
3.4
0.0
30.9
142.8
% of Classes Under 20
-0.171
0.205
-0.838
0.417
-0.613
0.271
% of Classes of 50 or More
-0.266
0.387
-0.688
0.503
-1.102
0.570
-0.127
0.099
-1.276
0.224
-0.341
0.088
Acceptance Rate
1st-Year Students in Top 10% of HS
Class
0.116
0.089
1.304
0.215
-0.076
0.308
2.075
4.018
0.516
0.614
-6.607
10.756
Academic Reputation Score
-0.532
0.408
-1.305
0.215
-1.413
0.349
Student/Faculty Ratio
Transcribed Image Text:SUMMARY OUTPUT
Regression Statistics
Multiple R
0.821
R Square
0.673
Adjusted R Square
0.564
Standard Error
2.52
Observations
25
ANOVA
df
F
Significance F
SS
MS
Regression
6.
236.32
39.39
6.18
0.0012
Residual
18
114.64
6.37
Total
24
350.96
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
70.26
10.59
6.63
0.00
48.01
92.51
0.021
0.087
0,241
0.812
-0.161
0.203
% of Classes Under 20
-0.013
0.221
-0.060
0.953
-0.478
0.452
% of Classes of 50 or More
-0.159
0.055
-2,907
0.009
-0.274
-0.044
Acceptance Rate
1st-Year Students in Top 10% of HS
0.142
0.090
1.589
0.129
-0.046
0.330
Class
1.278
1.947
0.656
0.520
-2.812
5.368
Academic Reputation Score
0.688
0.268
2.563
0.020
0.124
1.251
Student/Faculty Ratio
a)
What is heteroscedasticity?
b) Why is heteroscedasticity a problem?
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